Dec 29 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 can only be <9>
R5C5 can only be <4>
R8C5 can only be <1>
R6C5 can only be <6>
R1C4 can only be <6>
R1C6 can only be <8>
R4C5 can only be <8>
R4C6 can only be <3>
R4C1 can only be <4>
R4C9 can only be <7>
R9C6 can only be <9>
R5C4 can only be <7>
R6C4 can only be <9>
R4C4 can only be <1>
R9C4 can only be <3>
R3C1 is the only square in row 3 that can be <8>
R7C9 is the only square in row 7 that can be <9>
R1C8 is the only square in row 1 that can be <9>
R9C2 is the only square in row 9 that can be <8>
Squares R2C2 and R5C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C2 - removing <5> from <245> leaving <24>
R8C2 - removing <3> from <234> leaving <24>
Squares R5C8 and R8C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C8 - removing <3> from <137> leaving <17>
Intersection of row 3 with block 3. The value <2> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C7 - removing <2> from <247> leaving <47>
R1C9 - removing <2> from <1245> leaving <145>
Squares R1C7 and R9C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C7 - removing <4> from <234> leaving <23>
R7C7 - removing <7> from <237> leaving <23>
Squares R7C7 and R8C8 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C9 - removing <23> from <2346> leaving <46>
Intersection of row 7 with block 7. The value <7> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C1 - removing <7> from <567> leaving <56>
R9C3 - removing <7> from <457> leaving <45>
Squares R3C3 and R7C3 in column 3 and R3C7 and R7C7 in column 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 3 and 7 can be removed.
R7C1 - removing <3> from <237> leaving <27>
R3C9 - removing <3> from <234> leaving <24>
Squares R3C3 (XY), R2C2 (XZ) and R9C3 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R1C3 - removing <5> from <457> leaving <47>
R9C3 is the only square in column 3 that can be <5>
R9C1 can only be <6>
R8C9 is the only square in row 8 that can be <6>
R8C2 is the only square in row 8 that can be <4>
R1C2 can only be <2>
Squares R1C3 and R1C7 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C1 - removing <7> from <157> leaving <15>
R1C9 - removing <4> from <145> leaving <15>
Squares R6C9 and R8C1 form a remote naked pair. <23> can be removed from any square that is common to their groups.
R6C1 - removing <3> from <35> leaving <5>
R6C6 can only be <2>
R1C1 can only be <1>
R5C2 can only be <3>
R6C9 can only be <3>
R5C6 can only be <5>
R5C8 can only be <2>
R1C9 can only be <5>
R2C9 can only be <1>
R2C8 can only be <7>
R9C9 can only be <4>
R2C2 can only be <5>
R8C8 can only be <3>
R8C1 can only be <2>
R7C7 can only be <2>
R9C7 can only be <7>
R3C9 can only be <2>
R2C1 can only be <3>
R9C8 can only be <1>
R1C7 can only be <4>
R3C7 can only be <3>
R7C1 can only be <7>
R1C3 can only be <7>
R3C3 can only be <4>
R7C3 can only be <3>
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